Digital-electronics 简明教程
Universal Gates NAND and NOR
能够实现任何可能的布尔函数的逻辑门称为 universal gate 。有两种通用逻辑门，即 NAND 门和 NOR 门。
A logic gate that can implement any kind of possible Boolean function is called a universal gate. There are two universal logic gates namely, NAND gate and NOR gate.
这两个门被称为通用门，因为它们可以在不需要任何其他类型逻辑门的情况下执行 AND、OR、NOT、XOR 和 XNOR 等任何其他逻辑门的功能。例如，我们可以仅使用 NAND 门或仅使用 NOR 门执行 AND 门函数。
These two gates are called universal gates because they can perform the function of any other logic gate like AND, OR, NOT, XOR, and XNOR without need of any other type of logic gate. For example, we can perform the AND gate function by using only NAND gates or only NOR gates.
在本章中，我们将学习通用门的理论和原理，即 NAND 门和 NOR 门。
In this chapter, we will study the theory and working of the universal gates, i.e., NAND gate and NOR gate.
What is a NAND Gate?
NAND gate 是一个通用门，基本上是两个基本逻辑门的组合，即 AND 门和 NOT 门。它是由将 NOT 门连接到 AND 门的输出线而设计的，如图所示。
The NAND gate is a universal gate that basically a combination of two basic logic gates namely, AND gate and NOT gate. It is designed by connecting a NOT gate to the output line of the AND gate, as shown in the following figure.
NAND 门可以有两个或多个输入线和一个输出线。仅当 NAND 门的所有输入都为高电平或逻辑 1 时，该门输出才会为低电平或逻辑 0。否则，NAND 门的输出将为高电平或逻辑 1。
The NAND gate can have two or more input lines and one output line. The output of the NAND gate is low or logic 0 only when all its inputs are high or logic 1. Otherwise, the output of the NAND gate is high or logic 1.
NAND 门基本上是一个执行 AND 门逆操作的逻辑门。
The NAND gate is basically a logic gate that performs the inverse operation of an AND gate.
作为通用门，NAND 门可以实现任何可能的布尔函数或任何其他类型逻辑门的操作。
Being a universal gate, the NAND gate can implement any possible Boolean function or operation of any other type of logic gate.
Logic Symbol of NAND Gate
两输入和三输入 NAND 门的逻辑符号如下图所示。
The logic symbols of a two-input and three-input NAND gates are depicted in the following figure.
这里，输出端的圆圈表示反转操作。
Here, the bubble at the output side represents the inversion operation.
变量 A、B 和 C 指定输入线，变量 Y 表示 NAND 门的输出线。
The variables A, B, and C designate the input lines and the variable Y represents the output line of the NAND gate.
Truth Table of NAND Gate
真值表是 NAND 门的输入和输出的表格，显示它们之间的关系。以下是 two-input NAND gate 的真值表
Truth table is a table of inputs and outputs of a NAND gate showing the relationship between them. Here is the truth table of a two-input NAND gate −
Input |
Output |
A |
B |
Y |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
three-input NAND gate 的真值表如下所示
The truth table for a three-input NAND gate is given below −
Input |
Output |
A |
B |
C |
Y |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
从这两个真值表中，我们可以观察到，只有当 NAND 门的所有输入都高或逻辑 1 时，它才会产生低电平或逻辑 0 输出。对于任何其他输入组合，输出都是高电平或逻辑 1。
From these two truth tables, we can observe that the NAND gate produces a low or logic 0 output only when all its inputs are high or logic 1. For any other input combinations, the output is high or logic 1.
Boolean Expression of NAND Gate
布尔表达式是描述 NAND 门的输入和输出之间的逻辑关系的逻辑函数。
The Boolean expression is a logical function that describes the logical relationship between inputs and output of a NAND gate.
双输入 NAND 门的布尔表达式如下所示
The Boolean expression for a two-input NAND gate is give below −
\mathrm{Y \: = \: \overline{AB} \: = \: (AB)'}
三输入 NAND 门的布尔表达式给出为
The Boolean expression for a three-input NAND gate is given by,
\mathrm{Y \: = \: \overline{ABC} \: = \: (ABC)'}
在此，A、B 和 C 是输入变量，Y 是输出变量。
Here, A, B, and C are the input variables and Y is the output variable.
Working of NAND Gate
双输入 NAND 门针对不同输入组合的工作方式如下所述
The working of a two-input NAND gate for different input combinations is described below −
-
If A = 0 and B = 0, the output of the NAND gate is Y = 1.
-
If A = 0 and B = 1, the output of the NAND gate is Y = 1.
-
If A = 1 and B = 0, the output of the NAND gate is Y = 1.
-
If A = 1 and B = 1, the output of the NAND gate is Y = 0.
类似地，三输入 NAND 门的工作方式可以解释如下
Similarly, the working of a three-input NAND gate can be explained as below −
-
If A = 0, B = 0, and C = 0 the output of the NAND gate is Y = 1.
-
If A = 0, B = 0, and C = 1 the output of the NAND gate is Y = 1.
-
If A = 0, B = 1, and C = 0 the output of the NAND gate is Y = 1.
-
If A = 0, B = 1, and C = 1 the output of the NAND gate is Y = 1.
-
If A = 1, B = 0, and C = 0 the output of the NAND gate is Y = 1.
-
If A = 1, B = 0, and C = 1 the output of the NAND gate is Y = 1.
-
If A = 1, B = 1, and C = 0 the output of the NAND gate is Y = 1.
-
If A = 1, B = 1, and C = 1 the output of the NAND gate is Y = 0.
此示例介绍了 NAND 门在不同输入组合下的操作方式。
This is all about the operation of a NAND gate for different input combinations.
同样重要的是，在本节中，我们将仅针对两个和三个输入变量讨论 NAND 门的理论。但相同的逻辑和理论适用于任意数量的输入。
It is also important to note that in this chapter, we are discussing the theory of NAND gate by considering only two and three input variables. But the same logic and theory is applicable to any number of inputs.
NAND Gate using Transistor
我们可以使用 BJT 晶体管来实现 NAND 门逻辑。这样的 NAND 门称为 transistor NAND gate 。
We can implement the NAND gate logic by using BJT transistors. Such a NAND gate is referred to as a transistor NAND gate.
双输入 NAND 门的晶体管电路图如下图所示。
The transistor circuit diagram of a two-input NAND gate is shown in the following figure.
Working of Transistor NAND Gate
此晶体管 NAND 门针对不同输入组合的工作原理说明如下：
The working of this transistor NAND gate for different input combinations is explained below −
When both inputs A and B are connected to a low signal ，晶体管 Q1 和 Q2 充当开路开关。整个电源电压将出现在输出线路 Y 处。因此，对于这种情况组合，电路的输出为高电平或逻辑 1。
When both inputs A and B are connected to a low signal, the transistors Q1 and Q2 act as open switches. The entire supply voltage will appear at the output line Y. Hence, for this input combination, the output of the circuit is high or logic 1.
When the input A is at low level and the input B is at high level ，晶体管 Q1 充当开路开关，晶体管 Q2 充当闭合开关。在这种情况下，电源和接地端之间没有直接连接。因此，整个电源电压将出现在输出端 Y 上，使其变为高电平或逻辑 1。
When the input A is at low level and the input B is at high level, the transistor Q1 acts as an open switch and the transistor Q2 acts as a closed switch. In this case, there is not a direct connection between power supply and the ground terminal. Hence, the whole supply voltage will appear at the output terminal Y, making it high or logic 1.
When the input A is at high level and the input B is at low level ，晶体管 Q1 充当闭合开关，晶体管 Q2 充当开路开关。同样，电源和接地端之间会断开。对于这种情况组合，整个电源电压将出现在输出线路处，并将输出设为高电平或逻辑 1。
When the input A is at high level and the input B is at low level, the transistor Q1 acts as a closed switch and the transistor Q2 acts as an open switch. Again, there is a disconnection between power supply and the ground terminal. For this combination of inputs, the entire supply voltage will appear at the output line and sets the output high or logic 1.
When the both inputs are connected to a high or logic 1 signal ，两个晶体管都将导通，并将输出线直接连接到接地端，即低电位。这将使电路的输出变为低电平或逻辑 0。
When the both inputs are connected to a high or logic 1 signal, both transistors will turn on and connects the output line directly to the ground terminal i.e., to a low potential. This makes the output of the circuit low or logic 0.
因此，只有当所有输入均为高电平或逻辑 1 时，此电路的输出才会变为低电平或逻辑 0，否则输出将为高电平或逻辑 1。因此，此电路实现了 NAND 门逻辑。
Hence, the output of this circuit is low or logic 0, only when all inputs are high or logic 1, otherwise the output is high or logic 1. Thus, this circuit implements the NAND gate logic.
NAND Gate using Switches
我们还可以使用电气开关、电池和灯泡来实现 NAND 门。使用开关的两输入 NAND 门的电路图如下图所示。
We can also realize the NAND gate using electric switches, a battery, and a lamp. The circuit diagram of a two-input NAND gate using switches is shown in the following figure.
在此开关电路中，当两个开关 A 和 B 都闭合时，有一个绕过灯泡的短路电流流过路径。因此，不会有电流流过灯泡，灯泡不会发光。这表示低电平或逻辑 0 输出。
In this switching circuit, when both switches A and B are closed, there is a short-circuited path for the flow of electric current that bypasses the lamp. Hence, no current will flow through the lamp and the lamp will not glow. This represents the low or logic 0 output.
对于任何其他开关布置，例如 A 闭合且 B 开启，A 开启且 B 闭合，或者 A 和 B 开启。没有短路路径，并且整个电流将流过灯泡，使其点亮。这表示高电平或逻辑 1 输出。
For any other switching arrangement, such as A is closed and B is open, A is open and B is closed, or A and B are open. There is no short-circuited path and the entire current will flow through the lamp, making it turn on. This represents the high or logic 1 output.
因此，只有当两个开关都闭合时，此开关电路的输出才变为低电平或逻辑 0，否则输出为高电平或逻辑 1。因此，此电路可充当 NAND 门。
Thus, the output of this switching circuit is low or logic 0 only when both switches are closed, otherwise the output is high or logic 1. Hence, this circuit acts as a NAND gate.
我们可以串联添加更多开关到 A 和 B 来实现更高阶的 NAND 门。
We can add more switches in series with A and B to implement a higher order NAND gate.
NAND Gate as an Inverter
NAND 门也可以用作反相器门。为此，它的所有输入都连接在一起，并且要反转的输入信号被应用于公共端，如下图所示。
The NAND gate can also be used as an inverter gate. For this, all its inputs are joined together and the input signal to be inverted is applied to the common terminal as shown in the following figure.
Applications of NAND Gate
NAND 门用于各种数字和自动系统中。其中一些列在下面 −
The NAND gate is used in a variety of digital and automated systems. Some of them are listed below −
-
Alarm circuits
-
Buzzer and burglar devices
-
Automatic temperature regulation systems
-
Security systems
-
Automated doors and windows, etc.
上面就是关于 NAND 门、其工作和应用的所有内容。现在让我们讨论另一个通用门（称为 NOR 门）的原理。
This is all about the NAND gate, its working and applications. Let us now discuss the theory of another universal gate named, NOR gate.
What is a NOR Gate?
NOR gate 是数字电子设备中用于实现布尔函数的另一个通用门。它是两个基本逻辑门的组合，即 OR 门和 NOT 门。NOR 门的设计是将 NOT 门连接到输出线，并且最终输出从 NOT 门的输出线获取，如下图所示。
The NOR gate is another universal gate used in digital electronics to implement Boolean functions. It is a combination of two basic logic gates namely, OR gate and NOT gate. The NOR gate is designed by connecting a NOT gate to the output line and the final output is taken from the output line of the NOT gate as shown in the following figure.
作为一个通用逻辑门，它可以单枪匹马地用于实现任何可能的布尔函数或其他逻辑门。
Being a universal logic gate, it can be used to implement any possible Boolean function or the other logic gates single-handedly.
NOR 门可以有两个或更多个输入线和一个输出线。只有当所有输入都为低或逻辑 0 时，NOR 门的输出才为高或逻辑 1。对于所有其他输入组合，NOR 门的输出都为低或逻辑 0。
The NOR gate can have two or more input lines and one output line. The output of the NOR gate is high or logic 1 only when all its inputs are low or logic 0. For all other input combinations, the output of the NOR gate is low or logic 0.
Logic Symbol of NOR Gate
一个双输入和一个三输入 NOR 门的逻辑符号如下图所示。
The logic symbols of a two-input and three-input NOR gates are shown in the following figure.
这里，A、B 和 C 是输入线，Y 是输出线。输出端的圆圈表示反转运算。
Here, A, B, and C are the input lines and Y is the output line. The bubble at the output end represents the inversion operation.
Truth Table of NOR Gate
NOR 门的真值表规定了不同输入组合的输出。一个双输入 NOR 门的真值表如下 −
The truth table of the NOR gate specifies the output for different input combinations. The truth table of a two-input NOR gate is given below −
Input |
Output |
A |
B |
Y |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
以下是三输入 NOR 门的真值表 −
The following is the truth table of a three-input NOR gate −
Input |
Output |
A |
B |
C |
Y |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
从这些真值表中，我们可以观察到 NOR 门的输出仅在所有输入都为低或逻辑 0 时为高或逻辑 1，否则输出为低或逻辑 0。
From these truth tables, we can observe that the output of the NOR gate is high or logic 1 only when all its inputs are low or logic 0, otherwise the output is low or logic 0.
Working of NOR Gate
下面解释了两个输入 NOR 门在所有可能的输入组合中的运算 −
The operation of a two-input NOR gate for all possible input combinations is explained below −
-
If A = 0 and B = 0, the output of the NOR gate is Y = 1.
-
If A = 0 and B = 1, the output of the NOR gate is Y = 0.
-
If A = 1 and B = 0, the output of the NOR gate is Y = 0.
-
If A = 1 and B = 1, the output of the NOR gate is Y = 0.
类似地，可以描述三个输入 NOR 门的运算，如下 −
Similarly, the operation of the three-input NOR gate can be described, as below −
-
If A = 0, B = 0, and C = 0 the output of the NOR gate is Y = 1.
-
If A = 0, B = 0, and C = 1 the output of the NOR gate is Y = 0.
-
If A = 0, B = 1, and C = 0 the output of the NOR gate is Y = 0.
-
If A = 0, B = 1, and C = 1 the output of the NOR gate is Y = 0.
-
If A = 1, B = 0, and C = 0 the output of the NOR gate is Y = 0.
-
If A = 1, B = 0, and C = 1 the output of the NOR gate is Y = 0.
-
If A = 1, B = 1, and C = 0 the output of the NOR gate is Y = 0.
-
If A = 1, B = 1, and C = 1 the output of the NOR gate is Y = 0.
从这一讨论中，我们可以观察到，当所有输入都是低电平或逻辑 0 时，NOR 门产生高电平或逻辑 1 输出。
From this discussion, we can observe that the NOR gate produces a high or logic 1 output when all its inputs are low or logic 0.
NOR Gate using Transistor
我们可以使用晶体管来实现 NOR 门。使用晶体管实现的双输入 NOR 门电路图如下图所示。此电路被称为 transistor NOR gate 。
We can implement the NOR gate using transistors. The circuit diagram of a two-input NOR gate using transistors is shown in the following figure. This circuit is known as transistor NOR gate.
Working of Transistor NOR Gate
晶体管 NOR 门的工作原理如下所示：
The working of the transistor NOR gate is explained below −
When both inputs A and B are low ，晶体管 Q1 和 Q2 不导通，并充当开路开关。在这种情况下，输出线 Y 将直接连接到电源。因此，整个电源电压将出现在输出端子上。这使得电路的输出变为高电平或逻辑 1。
When both inputs A and B are low, the transistors Q1 and Q2 do not conduct and act as open switches. In this case, the output line Y will directly connect to the power supply. Thus, the whole supply voltage will appear at the output terminal. This makes the output of the circuit high or logic 1.
When the input A is connected to low and the input B is connected to a high signal ，晶体管 Q1 将充当开路开关，而晶体管 Q2 将充当闭路开关。在这种情况下，输出线 Y 将通过晶体管 Q2 直接连接到接地端子上。这导致输出线上的信号变低。
When the input A is connected to low and the input B is connected to a high signal, the transistor Q1 will act as an open switch while the transistor Q2 will act as a closed switch. In this case, the output line Y will directly connect to the ground terminal through the transistor Q2. This results in a low signal at the output line.
When the input A is connected to high and the input B is connected to a low signal ，晶体管 Q1 将导通，而晶体管 Q2 将充当开路开关。在这种情况下，输出线直接连接到接地端子上。因此，输出为低电平或逻辑 0。
When the input A is connected to high and the input B is connected to a low signal, the transistor Q1 will conduct and the transistor Q2 will act as an open switch. In this case, the output line is directly connected to the ground terminal. Thus, the output is low or logic 0.
When both inputs A and B are connected to a high signal ，晶体管 Q1 和 Q2 都将充当闭路开关，并将输出线直接连接到接地端子上。在这种情况下，输出也是低电平或逻辑 0。
When both inputs A and B are connected to a high signal, both transistors Q1 and Q2 will act as closed switches and connect the output line directly to the ground terminal. In the case also, the output is low or logic 0.
从这一讨论中，我们可以观察到，此晶体管电路实现了 NOR 逻辑，因此被称为晶体管 NOR 门。
From this discussion, we can observe that this transistor circuit implements the NOR logic and hence called as transistor NOR gate.
我们可以向电路中添加更多晶体管以获得更高阶的 NOR 门。
We can add more transistors to the circuit to obtain a higher order NOR gate.
NOR Gate using Switches
我们还可以使用电气开关实现 NOR 门。使用开关实现的双输入 NOR 门的电路图如下图所示。
We can also realize the NOR gate using electrical switches. A circuit diagram for a two-input NOR gate using switches is shown in the following figure.
在此电路中，如果开关 A 和 B 都处于打开状态，则整个电流都将流过灯泡并将其点亮。这表示输出的高电平或逻辑 1 状态。
In this circuit, if both switches A and B are open, the entire current flows through the lamp and turn it on. This represents the high or logic 1 state of the output.
如果任一开关或两者关闭，则存在电流的短路路径，该路径绕过了灯泡。在这种情况下，灯泡不会发光，并表示输出的低或逻辑 0 状态。
If both or any of the switches is closed, there is a short-circuited path for the flow of current that bypasses the lamp. In this case, the lamp will not glow and represent the low or logic 0 state of the output.
因此，此开关电路的输出仅在两个输入均为低（即打开开关）时才为高或逻辑 1，否则输出为低或逻辑 0。
Thus, the output of this switching circuit is high or logic 1, only when both of its inputs are low i.e., open switches, otherwise the output is low or logic 0.
因此，该电路实现了 NOR 或逻辑门操作。
Therefore, this electric circuit realizes the NOR gate operation and logic.
NOR Gate as an Inverter
NOR 门也可以作为反相器门。为了将 NOR 门用作反相器，将所有输入连接在一起，并将输入信号施加到共用端，如下图所示。
The NOR gate also be operated as an inverter gate. To use the NOR gate as an inverter, all its inputs are connected together and the input signal is applied to the common terminal as shown in the following figure.
Applications of NOR Gate
NOR 门用于许多数字系统。以下是 NOR 门的一些常见应用：
The NOR gate is used in numerous digital systems. Some common applications of NOR gate are listed below −
-
Various digital systems
-
Industrial automation and control systems
-
Traffic control systems
-
Alarm circuits
-
Digital arithmetic circuits like adders and subtractors, etc.
Conclusion
总之，通用逻辑门能够实现任何可能的布尔函数或其他逻辑门，而无需任何其他类型的逻辑门。在数字电子学中，有两个通用逻辑门，即 NAND 门和 NOR 门。
In conclusion, a universal logic gate is one that can implement any possible Boolean functions or other logic gates without need of any other type of logic gates. In digital electronics, there are two universal logic gates namely, NAND gate and NOR gate.
在本节中，我们解释了这两个通用门的原理、工作原理和应用。在这里，我们只介绍了两个和三个输入的 NAND 和 NOR 门，但相同的原理和说明也同样适用于具有三个以上输入的 NAND 和 NOR 门。
In this chapter, we explained the theory, working, and applications of these two universal gates. Here, we covered only two and three-input NAND and NOR gates, but the same theory and explanation is equally valid for NAND and NOR gates with more than three inputs.